As the French-led offensive against Islamist militants in Mali advances, diplomats and intelligence officials in Paris are beginning to tamp down expectations that eliminating al-Qaeda-linked extremism in the region can be achieved anytime soon. Despite the military operation continuing to inflict heavy losses on jihadi combatants hunkered down in northern Mali’s mountainous border area, they say, the amorphous terrorist threat those extremists pose makes full military victory a relative notion.

“Final success in this case probably comes in us decimating Islamists in Mali, and send them scattering to open, unsecured parts of the Sahel — where their ability to organize and execute terror is greatly diminished,” says a French intelligence official who agreed to speak to TIME on the condition of anonymity. “This intervention has cost the Islamists very dearly, and they’re now dug in and trying to survive. But it’s also evident they have no intention of being taken alive, and will die fighting to avoid that if necessary. This unfortunately isn’t an enemy you can eliminate in a single operation.”

That caution tempers France’s recent victories in northern Mali. On March 5, French officials revealed that operations by some 1,600 French and Chadian special forces the previous night had killed around 15 extremists. That followed news on March 3 that some 50 radicals had been slain in heavy fighting that also claimed the life of the third French soldier since the intervention began Jan. 11.

Earlier battles left scores of jihadi fighters dead — including a series of skirmishes in late February that Chadian officials say killed at least 93 extremists. Those numbers are considerable given estimates by some French military commanders that between 1,200 and 1,500 Islamist fighters are active in Mali — a figure the French intelligence officer calls “closer probably to 800 or 900.”

Two commanders of al-Qaeda-allied Islamist militias in the Sahel are rumored to have died in recent battles. Authorities in Chad say their troops gunned down al-Qaeda in Islamic Maghreb (AQIM) regional leader Abdelhamid Abou Zeid — a brutal terrorist and kidnapper whose group is holding many of the 37 Western hostages currently detained by Islamists in Africa. Officials in Paris say they can’t confirm that Abou Zeid is dead, but on March 4 the head of France’s armed forces called his death “probable.”

Also unconfirmed are claims Chadian soldiers killed Mokhtar Belmokhtar, leader of an AQIM splinter group that took responsibility for the January terrorist strike on an Algerian natural-gas complex that killed 37 foreigners. Despite photographs published by Paris Match on March 5 purportedly showing Belmokhtar’s body, authorities in Paris continue to treat the reports as unconfirmed.

French officials have been hesitant to talk about the alleged deaths of Sahel extremist leaders in part to avoid provoking the ire of radicals holding 15 French citizens hostage in Africa. But that lack of swagger also reflects desire in Paris to avoid overselling security advances made in the push against North African extremists, which could bait their backers elsewhere into retaliatory action.

“We’re not calling this a ‘war on terror,’ and we don’t have decks of cards with photos of Islamists on them so the public can keep track of our progress,” says the French intelligence official, referring to the playing cards American authorities used during the Iraq war to rank the importance of targeted Iraqi officials. “Personalizing this operation would be a distraction from its basic objective. We want to reduce the ability of terrorist groups to operate and minimize the threat they pose to Africa, Europe and the world. If we do that by killing their leaders, that’s great — but not required if the wider objective can be attained.”

“Being able to wave Abou Zeid’s head on a stick or show the world Belmokhtar’s scalp would be a bigger media and political production than it would a decisive security breakthrough,” adds a French diplomat, who also spoke on the condition of anonymity. “They are very capable, influential leaders, but their armed backers and wider base of support are the more important targets. And we’re inflicting some really, heavy-duty damage to those targets.”

Officials in France’s intelligence and security services say the best-case scenario for the operation is to disrupt the jihadis’ infrastructure by depleting their arms and transport reserves and scatter them across the Sahel area sealed in by national borders. Virtually no one believes radical groups can be fully eliminated, nor their criminal activity entirely stomped out. But by reducing their forces — and disrupting their abilities to interact with the wider world — many officials think Africa will be more secure.

“From there, the challenge really lies in regional African nations taking over and creating the kind of political stability and popular support that deprives Islamists the anger and recruits they need to expand,” the intelligence official says. “The problem is, we’ve been waiting for that to happen for years, and there are already signs the rapid gains made against extremists militias are already leading some regional capitals to figure the threat is passed — it’s back to business as usual.”